瞎JB逆

P为质

const int mod = 1000000009;  
long long quickpow(long long a, long long b) {  
    if (b < 0) return 0;  
    long long ret = 1;  
    a %= mod;  
    while(b) {  
        if (b & 1) ret = (ret * a) % mod;  
        b >>= 1;  
        a = (a * a) % mod;  
    }  
    return ret;  
}  
long long inv(long long a) {  
    return quickpow(a, mod - 2);  
}  

N，P互质

ll extend_gcd(ll a, ll b, ll &x, ll &y) {  
    if (b == 0) {  
        x = 1, y = 0;  
        return a;  
    }  
    else {  
        ll r = extend_gcd(b, a % b, y, x);  
        y -= x * (a / b);  
        return r;  
    }  
}  
ll inv(ll a, ll n) {  
    ll x, y;  
    extend_gcd(a, n, x, y);  
    x = (x % n + n) % n;  
    return x;  
}  

逆元筛

const int mod = 1000000009;  
const int maxn = 10005;  
int inv[maxn];  
inv[1] = 1;  
for(int i = 2; i < 10000; i++)  
    inv[i] = inv[mod % i] * (mod - mod / i) % mod;  

阶乘逆元筛(阶乘数组：fac[ ])

fac[0]=fac[1]=1;

for(int i=2;i<=MAXN;i++)fac[i]=fac[i-1]*i%mod;

inv[MAXN]=quipow(fac[MAXN],mod-2);

for(int i=MAXN-1;i>=0;i--)inv[i]=inv[i+1]*(i+1)%mod;